CCSS.Math.Content.7.EE.A.1
The Standard
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Common Core State Standards for Mathematics · Expressions and Equations
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite linear expressions without changing their value. They use distribution, factoring, and combining like terms with whole numbers, fractions, decimals, and negative coefficients.
What Mastery Looks Like
- Students correctly expand, combine, subtract, and factor expressions that include fractions, decimals, and negative numbers. They can show that two forms are equivalent and name the property that connects them.
Common Misconceptions
- Students often distribute a coefficient to the first term only, or lose a negative sign when subtracting an expression. They may combine unlike terms, such as 3x and 4, or mishandle fraction multiplication. Some think factored and expanded forms cannot be equal because they look different.
How to Assess It
- Exit ticket: Rewrite 3/4(8x - 12) - 1/2(2x - 6) in simplest form. Label the property used in your first step.
Lesson moves
Ways to Teach It
Use algebra tiles with fraction coefficient cards to build 1/2(6x + 4), then rearrange the model to show 3x + 2.
Ask students to explain whether -2(3x - 5) and -6x - 10 are equivalent, then correct the false claim.
Give pairs expression cards and have teams race to match factored forms, expanded forms, and simplified forms.
Compare two phone plans written as 0.10(50 + x) and 5 + 0.10x, then explain why the costs match.
Free download
Printable 7.EE.A.1 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.7.EE.A.1, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
See the whole path on the Expressions & Equations progression map.
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.6.EE.A.3
Students must use distributive, associative, and commutative properties to rewrite expressions before extending them to rational linear expressions.
- CCSS.Math.Content.6.EE.A.2
Students use variable expression notation and meaning from 6.EE.A.2 before rewriting linear expressions with operation properties.
- CCSS.Math.Content.7.NS.A.3
Expanding, factoring, and combining like terms with rational coefficients require accurate addition, subtraction, multiplication, and division of rational numbers.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.8.EE.C.7b
Solving these equations requires distributing, expanding, and combining linear expressions with rational coefficients before isolating the variable.
- CCSS.Math.Content.8.EE.C.7
Solving linear equations often requires distributing, factoring, and combining rational linear expressions from both sides of the equation.
- CCSS.Math.Content.8.EE.C.8
Simplifying, expanding, and factoring linear expressions supports substitution and elimination when solving systems with rational coefficients.
- CCSS.Math.Content.8.EE.C.7a
Simplifying equations to x = a, a = a, or a = b requires distributing and combining linear expressions with rational coefficients.
- CCSS.Math.Content.7.EE.A.2
Using properties to expand, factor, and combine expressions supports interpreting how equivalent forms show different relationships in context.
- CCSS.Math.Content.HSA-APR.A.1
Combining and expanding linear expressions gives the distributive and like-term reasoning needed for polynomial operations.
Keep exploring
Related Standards
- CCSS.Math.Content.3.OA.B.5
Apply properties of operations as strategies to multiply and divide.
- CCSS.Math.Content.7.NS.A.1d
Apply properties of operations as strategies to add and subtract rational numbers.
- CCSS.Math.Content.7.NS.A.2c
Apply properties of operations as strategies to multiply and divide rational numbers.
- CCSS.Math.Content.1.OA.B.3
Apply properties of operations as strategies to add and subtract.
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